Sampled-data observer-based exponential stabilization of nonlinear systems with an application to tumor control

Ensuring stability in control systems with incomplete state information poses a significant challenge. This paper addresses this issue for nonlinear systems by leveraging the power of state observers and fast sampling. We demonstrate the following result: if the linearized system exhibits the standard structural properties of stabilizability and detectability, then the sampled-data Euler emulation of a continuous-time (Luenberger) observer-based stabilizer, designed for the linear continuous-time system, also guarantees local exponential convergence to the origin of the nonlinear system state, provided that sampling is sufficiently fast. While the result may seem expected, our work moves beyond conjecture by providing a rigorous proof that establishes this convergence under minimal assumptions. Unlike many approaches that require numerous strong assumptions for global guarantees, we forgo these requirements and accept a local result, which is still valuable in applications where understanding the system behavior around specific points is crucial. As an illustrative example, we show an application of the method to the control of the Hahnfeldt's model of colon tumor angiogenesis, showing the potential and effectiveness of the proposed approach.